Related papers: A short note on cospectral and integral chain grap…
The spectrum of the normalized Laplacian matrix cannot determine the number of edges in a graph, however finding constructions of cospectral graphs with differing number of edges has been elusive. In this paper we use basic properties of…
Over forty years ago, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph $X$ contains a Hadamard matrix then $X$ is either of Latin square type or of negative Latin square type. We extend their result to…
Cospectral graphs are a fascinating concept in graph theory, where two non-isomorphic graphs possess identical sets of eigenvalues. In this paper, we compute the $A_\alpha$-characteristic polynomial of neighbour and non-neighbour splitting…
We introduce and develop equivalent spectral graph theory for several fundamental graph cut problems including maxcut, mincut, Cheeger cut, anti-Cheeger cut, dual Cheeger problem and their useful variants. A specified strategy for achieving…
We prove an upper bound on the number of pairwise strongly cospectral vertices in a normal Cayley graph, in terms of the multiplicities of its eigenvalues. We use this to determine an explicit bound in Cayley graphs of $\mathbb{Z}_2^d$ and…
New criteria for which Cayley graphs of cyclic groups of any order can be completely determined--up to isomorphism--by the eigenvalues of their adjacency matrices is presented. Secondly, a new construction for pairs of nonisomorphic Cayley…
We examine the capacity of the complementarity spectrum to distinguish non-isomorphic digraphs. We focus on the seven families with exactly three complementarity eigenvalues. Our findings reveal that in some, but not all families, any two…
The search for a highly discriminating and easily computable invariant to distinguish graphs remains a challenging research topic. Here we focus on cospectral graphs whose complements are also cospectral (generalized cospectral), and on…
For given k distinct complex conjugate pairs, l distinct real numbers, and a given graph G on 2k+l vertices with a matching of size at least k, we will show that there is a real matrix whose eigenvalues are the given numbers and its graph…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
It is shown that for a given infinite graph $G$ on countably many vertices, and a compact, infinite set of real numbers $\Lambda$ there is a real symmetric matrix $A$ whose graph is $G$ and its spectrum is $\Lambda$. Moreover, the set of…
In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain $\Omega\subset {\mathbb R}^d$, $d\ge 1$. When $\Omega=[0,1]$, such graphs include the standard Toeplitz…
Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family…
In this paper, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
The spectral symbols are useful tools to analyse the eigenvalue distribution when dealing with high dimensional linear systems. Given a matrix sequence with an asymptotic symbol, the last one depends only on the spectra of the individual…
In this paper, we investigate various algebraic and graph theoretic properties of the distance matrix of a graph. Two graphs are $D$-cospectral if their distance matrices have the same spectrum. We construct infinite pairs of $D$-cospectral…
We continue the study of non-commutative operator graphs generated by resolutions of identity covariant with respect to unitary actions of the circle group and the Heisenber-Weyl group as well. It is shown that the graphs generated by the…
Recently the collection $\cal G$ of all signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to $\pm 1$ has been determined. Here we investigate $\cal G$ for cospectral pairs, and for signed graphs…
In this paper, we discuss maximality of Seidel matrices with a fixed largest eigenvalue. We present a classification of maximal Seidel matrices of largest eigenvalue $3$, which gives a classification of maximal equiangular lines in a…